Polytope of Type {94,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {94,6}*1128
Also Known As : {94,6|2}. if this polytope has another name.
Group : SmallGroup(1128,34)
Rank : 3
Schlafli Type : {94,6}
Number of vertices, edges, etc : 94, 282, 6
Order of s₀s₁s₂ : 282
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {94,2}*376
   6-fold quotients : {47,2}*188
   47-fold quotients : {2,6}*24
   94-fold quotients : {2,3}*12
   141-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 47)(  3, 46)(  4, 45)(  5, 44)(  6, 43)(  7, 42)(  8, 41)(  9, 40)
( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)( 17, 32)
( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 49, 94)
( 50, 93)( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)( 57, 86)
( 58, 85)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)
( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 71, 72)( 96,141)( 97,140)
( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,132)
(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)(113,124)
(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)(145,186)
(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)
(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(190,235)(191,234)(192,233)(193,232)
(194,231)(195,230)(196,229)(197,228)(198,227)(199,226)(200,225)(201,224)
(202,223)(203,222)(204,221)(205,220)(206,219)(207,218)(208,217)(209,216)
(210,215)(211,214)(212,213)(237,282)(238,281)(239,280)(240,279)(241,278)
(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)(248,271)(249,270)
(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)(256,263)(257,262)
(258,261)(259,260);;
s1 := (  1,  2)(  3, 47)(  4, 46)(  5, 45)(  6, 44)(  7, 43)(  8, 42)(  9, 41)
( 10, 40)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 35)( 16, 34)( 17, 33)
( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)( 48, 96)
( 49, 95)( 50,141)( 51,140)( 52,139)( 53,138)( 54,137)( 55,136)( 56,135)
( 57,134)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)( 64,127)
( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121)( 71,120)( 72,119)
( 73,118)( 74,117)( 75,116)( 76,115)( 77,114)( 78,113)( 79,112)( 80,111)
( 81,110)( 82,109)( 83,108)( 84,107)( 85,106)( 86,105)( 87,104)( 88,103)
( 89,102)( 90,101)( 91,100)( 92, 99)( 93, 98)( 94, 97)(142,143)(144,188)
(145,187)(146,186)(147,185)(148,184)(149,183)(150,182)(151,181)(152,180)
(153,179)(154,178)(155,177)(156,176)(157,175)(158,174)(159,173)(160,172)
(161,171)(162,170)(163,169)(164,168)(165,167)(189,237)(190,236)(191,282)
(192,281)(193,280)(194,279)(195,278)(196,277)(197,276)(198,275)(199,274)
(200,273)(201,272)(202,271)(203,270)(204,269)(205,268)(206,267)(207,266)
(208,265)(209,264)(210,263)(211,262)(212,261)(213,260)(214,259)(215,258)
(216,257)(217,256)(218,255)(219,254)(220,253)(221,252)(222,251)(223,250)
(224,249)(225,248)(226,247)(227,246)(228,245)(229,244)(230,243)(231,242)
(232,241)(233,240)(234,239)(235,238);;
s2 := (  1,189)(  2,190)(  3,191)(  4,192)(  5,193)(  6,194)(  7,195)(  8,196)
(  9,197)( 10,198)( 11,199)( 12,200)( 13,201)( 14,202)( 15,203)( 16,204)
( 17,205)( 18,206)( 19,207)( 20,208)( 21,209)( 22,210)( 23,211)( 24,212)
( 25,213)( 26,214)( 27,215)( 28,216)( 29,217)( 30,218)( 31,219)( 32,220)
( 33,221)( 34,222)( 35,223)( 36,224)( 37,225)( 38,226)( 39,227)( 40,228)
( 41,229)( 42,230)( 43,231)( 44,232)( 45,233)( 46,234)( 47,235)( 48,142)
( 49,143)( 50,144)( 51,145)( 52,146)( 53,147)( 54,148)( 55,149)( 56,150)
( 57,151)( 58,152)( 59,153)( 60,154)( 61,155)( 62,156)( 63,157)( 64,158)
( 65,159)( 66,160)( 67,161)( 68,162)( 69,163)( 70,164)( 71,165)( 72,166)
( 73,167)( 74,168)( 75,169)( 76,170)( 77,171)( 78,172)( 79,173)( 80,174)
( 81,175)( 82,176)( 83,177)( 84,178)( 85,179)( 86,180)( 87,181)( 88,182)
( 89,183)( 90,184)( 91,185)( 92,186)( 93,187)( 94,188)( 95,236)( 96,237)
( 97,238)( 98,239)( 99,240)(100,241)(101,242)(102,243)(103,244)(104,245)
(105,246)(106,247)(107,248)(108,249)(109,250)(110,251)(111,252)(112,253)
(113,254)(114,255)(115,256)(116,257)(117,258)(118,259)(119,260)(120,261)
(121,262)(122,263)(123,264)(124,265)(125,266)(126,267)(127,268)(128,269)
(129,270)(130,271)(131,272)(132,273)(133,274)(134,275)(135,276)(136,277)
(137,278)(138,279)(139,280)(140,281)(141,282);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(282)!(  2, 47)(  3, 46)(  4, 45)(  5, 44)(  6, 43)(  7, 42)(  8, 41)
(  9, 40)( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)
( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)
( 49, 94)( 50, 93)( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)
( 57, 86)( 58, 85)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)
( 65, 78)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 71, 72)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)
(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)
(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)
(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(190,235)(191,234)(192,233)
(193,232)(194,231)(195,230)(196,229)(197,228)(198,227)(199,226)(200,225)
(201,224)(202,223)(203,222)(204,221)(205,220)(206,219)(207,218)(208,217)
(209,216)(210,215)(211,214)(212,213)(237,282)(238,281)(239,280)(240,279)
(241,278)(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)(248,271)
(249,270)(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)(256,263)
(257,262)(258,261)(259,260);
s1 := Sym(282)!(  1,  2)(  3, 47)(  4, 46)(  5, 45)(  6, 44)(  7, 43)(  8, 42)
(  9, 41)( 10, 40)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 35)( 16, 34)
( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)
( 48, 96)( 49, 95)( 50,141)( 51,140)( 52,139)( 53,138)( 54,137)( 55,136)
( 56,135)( 57,134)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)
( 64,127)( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121)( 71,120)
( 72,119)( 73,118)( 74,117)( 75,116)( 76,115)( 77,114)( 78,113)( 79,112)
( 80,111)( 81,110)( 82,109)( 83,108)( 84,107)( 85,106)( 86,105)( 87,104)
( 88,103)( 89,102)( 90,101)( 91,100)( 92, 99)( 93, 98)( 94, 97)(142,143)
(144,188)(145,187)(146,186)(147,185)(148,184)(149,183)(150,182)(151,181)
(152,180)(153,179)(154,178)(155,177)(156,176)(157,175)(158,174)(159,173)
(160,172)(161,171)(162,170)(163,169)(164,168)(165,167)(189,237)(190,236)
(191,282)(192,281)(193,280)(194,279)(195,278)(196,277)(197,276)(198,275)
(199,274)(200,273)(201,272)(202,271)(203,270)(204,269)(205,268)(206,267)
(207,266)(208,265)(209,264)(210,263)(211,262)(212,261)(213,260)(214,259)
(215,258)(216,257)(217,256)(218,255)(219,254)(220,253)(221,252)(222,251)
(223,250)(224,249)(225,248)(226,247)(227,246)(228,245)(229,244)(230,243)
(231,242)(232,241)(233,240)(234,239)(235,238);
s2 := Sym(282)!(  1,189)(  2,190)(  3,191)(  4,192)(  5,193)(  6,194)(  7,195)
(  8,196)(  9,197)( 10,198)( 11,199)( 12,200)( 13,201)( 14,202)( 15,203)
( 16,204)( 17,205)( 18,206)( 19,207)( 20,208)( 21,209)( 22,210)( 23,211)
( 24,212)( 25,213)( 26,214)( 27,215)( 28,216)( 29,217)( 30,218)( 31,219)
( 32,220)( 33,221)( 34,222)( 35,223)( 36,224)( 37,225)( 38,226)( 39,227)
( 40,228)( 41,229)( 42,230)( 43,231)( 44,232)( 45,233)( 46,234)( 47,235)
( 48,142)( 49,143)( 50,144)( 51,145)( 52,146)( 53,147)( 54,148)( 55,149)
( 56,150)( 57,151)( 58,152)( 59,153)( 60,154)( 61,155)( 62,156)( 63,157)
( 64,158)( 65,159)( 66,160)( 67,161)( 68,162)( 69,163)( 70,164)( 71,165)
( 72,166)( 73,167)( 74,168)( 75,169)( 76,170)( 77,171)( 78,172)( 79,173)
( 80,174)( 81,175)( 82,176)( 83,177)( 84,178)( 85,179)( 86,180)( 87,181)
( 88,182)( 89,183)( 90,184)( 91,185)( 92,186)( 93,187)( 94,188)( 95,236)
( 96,237)( 97,238)( 98,239)( 99,240)(100,241)(101,242)(102,243)(103,244)
(104,245)(105,246)(106,247)(107,248)(108,249)(109,250)(110,251)(111,252)
(112,253)(113,254)(114,255)(115,256)(116,257)(117,258)(118,259)(119,260)
(120,261)(121,262)(122,263)(123,264)(124,265)(125,266)(126,267)(127,268)
(128,269)(129,270)(130,271)(131,272)(132,273)(133,274)(134,275)(135,276)
(136,277)(137,278)(138,279)(139,280)(140,281)(141,282);
poly := sub<Sym(282)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope